Direct-sequence code-division multiple-access (DS-CDMA) has become an important component of recent communication systems. This is due to its many attractive properties for wireless communications such as the one depicted in FIG. 1A. In DS-CDMA communications, users' signals are multiplexed by distinct code waveforms, rather than by orthogonal frequency bands in frequency-division multiple access (FDMA), or by orthogonal time slots in time-division multiple access (TDMA). All users can transmit at the same time with each of them being allocated the entire available, broad-band, frequency spectrum for transmission. This method of channel allocation alleviates the problems commonly associated with other forms of channel allocation such as unused resources.
In CDMA, demodulation requires the suppression of two forms of noise, ambient channel noise, which is modeled as additive white Gaussian noise, plus multiple access interference (MAI), which is highly structured. The conventional receiver, which uses a simple correlation of the received signal and its user-spreading sequence (a standard matched filter), does not take into account the existence of MAI. The MAI caused by any one user is generally small, but as the number of interferers and their total power increases, the effects of MAI can become substantial. These effects fall within, what is called, the near-far problem.
The conventional receiver is severely limited by the effects of such MAI. One way to alleviate the MAI problem is to use power control schemes. However, power control is not easy to accomplish, especially in a wireless environment, where the power levels often vary dramatically. Even if perfect power control is used, the system may still need to be implemented with a forward error-correcting code to obtain a good performance. Another way of handling the near-far problem is to use near-far resistant receivers, which, in principle, can yield a substantial improvement over the standard receiver with perfect power control.
Multiuser detection techniques were proposed many years ago to mitigate the MAI problem. For example, S. Verdú, in “Minimum probability of error for asynchronous gaussian multiple-access channels,” IEEE Trans. on Inform. Theory, vol. IT-32, pp. 85–96, January 1986, [1], the entire contents of which are hereby expressly incorporated by reference, proposed and found the optimal multiuser detection criterion and maximum-likelihood sequence detection for DS-CDMA. Unfortunately, Verdú's detection and demodulation methods were generally too complex to realize in a practical DS-CDMA system.
As a consequence, a number of simplified detector-demodulators have been proposed to obtain near optimal performance with reduced computational complexity. (For example, see R. Lupas and S. Verdú, “Linear multiuser detectors for synchronous code-division multiple-access channels,” IEEE Trans. On Inform. Theory, vol. 35, pp. 123–136, January 1989 [2]; R. Lupas and S. Verdú, “Near-far resistance of multiuser detectors in asynchronous channels,” IEEE Trans. on Commun., vol. 38, pp. 496–508, April 1990 [3]; Z. Xie, R. T. Short, and C. K. Rushforth, “A family of suboptimum detectors for coherent multiuser communications,” IEEE J. Select. Areas Commun., vol. 8, pp. 683–690, May 1990 [4]; U. Madhow and M. L. Honig, “MMSE interference suppression for direct-sequence spread spectrum CDMA,” IEEE Trans. On Commun., vol. 42, pp. 3178–31888, December 1994 [5]; M. L. Honig and J. S. Goldstein, “Adaptive reduced-rank residual correlation algorithms for DS-CDMA interference suppression,” in Conference Record of the Thirty-Second Asilomar Conference on Signals, Systems & Computers, 1998, vol. 1, pp. 551–555 [6]; and D. J. Lee, Adaptive Detection of DS/CDMA Signals Using Reduced-Rank Multistage Wiener Filter, Ph.D. thesis, University of Southern California, March 2000 [7], the contents of which are hereby expressly incorporated by reference.)
These receivers, however, deal primarily only with detectors that require a precise knowledge of the propagation delays of all users, which is usually unknown a priori. To use such an algorithm, the propagation delays need to be estimated and as a consequence, the receivers suffer from errors that occur with the estimation of the propagation delays. (See S. Parkvall, E. G. Strom, and B. Ottersten, “The impact of timing errors on the performance of linear ds-cdma receivers,” IEEE J. Select. Areas Commun., pp. 1660–1668, October 1996. [8], the contents of which are hereby expressly incorporated by reference). To obtain a better performance, the transmitters and receivers needed to be synchronized. Moreover, the transmitters and receivers, in this case, need to be synchronized in order to obtain a better performance. However, the synchronization requirement adds more complexity and cost to the system.
The conventional acquisition system that utilizes a tapped delay line with its weights being the elements of the spreading sequence also suffers from the same near-far problems. Many near-far resistant timing-acquisition algorithms have been developed. One approach is to jointly estimate the needed parameters of all users, as shown in Y. Steinberg and H. V. Poor, “On sequential delay estimation in wide-band digital communication systems,” in Proc. Intl. Symp. Information Theory, San Antonio, Tex., 1993, p. 423 [9]; and S. Y. Miller and S. C. Schwartz, “Parameter estimation for asynchronous multiuser communications,” in Proc. Conf. Information Sciences and Systems, Baltimore. Md., 1989, pp. 294–299 [10], the contents of which are hereby expressly incorporated by reference. While such techniques can provide excellent results, they are computationally complex.
Recently, maximum-likelihood synchronization of a single user is developed in S. E. Bensley and B. Aazhang. “Maximum-Likelihood synchronization of a single user for Code-Division Multiple-Access communication systems,” IEEE Trans. on Commun., pp. 392–399, March 1998 [11], the contents of which are hereby expressly incorporated by reference. However, the method in [11] requires a training period. This requirement is not feasible in certain situations. For example, whenever there is a significant change in the MAI level, during a deep fade or a turning-on of some near-in strong interferers, retraining is required, and the data transmission need to be interrupted accordingly. Similar limitations apply also to the minimum mean-square-error (MMSE) interference suppression techniques for the timing-acquisition, developed in U. Madhow, “MMSE interference suppression for timing acquisition and demodulation in Direct-Sequence CDMA systems,” IEEE Trans. on Commun., pp. 1065–1075, August 1998 [12], the contents of which are hereby expressly incorporated by reference.
By the use of a subspace decomposition technique, such as multiple signal classification (MUSIC), another type of timing estimator is developed in E. G. Ström, S. Parkvall, S. L. Miller, and B. E. Ottersten, “Propagation delay estimation in asynchronous direct-sequence code-division multiple access system,” IEEE Trans. on Commun., Vol. 44, pp. 84–93, January 1996 [13]; and S. E. Bensley and B. Aazhang, “Subspace-based channel estimation for code division multiple access communication systems,” IEEE Trans. on Commun., vol. 44, pp. 1009–1020, August 1996 [14], the contents of which are hereby expressly incorporated by reference. This type of estimator does not need a training sequence and provides good results when unknown information sequences are sent. However, this timing estimator still involves extensive computations due to the need for an eigen decomposition. Also, this technique assumes that the number of active users is fixed and needs to be known or estimated. As a result, there is a need for a system and method for a relatively simple, accurate, and cost effective filtering of an asynchronous wireless signal.